Measures on projectors of Jordan algebras of type I. (Russian) Zbl 0546.46053
The main result of the paper is the following generalization of the Gleason’s theorem in the case of JBW-algebras - Jordan analogues of abstract \(W^*\)-algebras:
Theorem. Let A be a JBW-algebra of type I without type \(I_ 2\) direct summands. Then any probability measure on projections of A can be uniquely extended to a normal state on A.
Theorem. Let A be a JBW-algebra of type I without type \(I_ 2\) direct summands. Then any probability measure on projections of A can be uniquely extended to a normal state on A.
Reviewer: Sh.A.Ayupor
MSC:
| 46L51 | Noncommutative measure and integration |
| 46L53 | Noncommutative probability and statistics |
| 46L54 | Free probability and free operator algebras |
| 46L30 | States of selfadjoint operator algebras |
| 17C65 | Jordan structures on Banach spaces and algebras |
| 17C50 | Jordan structures associated with other structures |
